On certain classes of close-to-convex functions
A function f, analytic in the unit disk E and given by , f(z)=z+∑k=2∞anzk is said to be in the family Kn if and only if Dnf is close-to-convex, where Dnf=z(1−z)n+1∗f, n∈N0={0,1,2,…} and ∗ denotes the Hadamard product or convolution. The classes Kn are investigated and some properties are given. It i...
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| Format: | Article |
| Language: | English |
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Wiley
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171293000390 |
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| _version_ | 1849410071411294208 |
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| author | Khalida Inayat Noor |
| author_facet | Khalida Inayat Noor |
| author_sort | Khalida Inayat Noor |
| collection | DOAJ |
| description | A function f, analytic in the unit disk E and given by , f(z)=z+∑k=2∞anzk is said to be
in the family Kn if and only if Dnf is close-to-convex, where Dnf=z(1−z)n+1∗f, n∈N0={0,1,2,…}
and ∗ denotes the Hadamard product or convolution. The classes Kn are investigated and some
properties are given. It is shown that Kn+1⫅Kn and Kn consists entirely of univalent functions.
Some closure properties of integral operators defined on Kn are given. |
| format | Article |
| id | doaj-art-764cff153a9049e3a38be8e24d49f1fc |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1993-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-764cff153a9049e3a38be8e24d49f1fc2025-08-20T03:35:16ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251993-01-0116232933610.1155/S0161171293000390On certain classes of close-to-convex functionsKhalida Inayat Noor0Mathematics Department, College of Science, P.O. Box 2455, King Saud University, Riyadh 11451, Saudi ArabiaA function f, analytic in the unit disk E and given by , f(z)=z+∑k=2∞anzk is said to be in the family Kn if and only if Dnf is close-to-convex, where Dnf=z(1−z)n+1∗f, n∈N0={0,1,2,…} and ∗ denotes the Hadamard product or convolution. The classes Kn are investigated and some properties are given. It is shown that Kn+1⫅Kn and Kn consists entirely of univalent functions. Some closure properties of integral operators defined on Kn are given.http://dx.doi.org/10.1155/S0161171293000390univalentclose-to-convexstarlikeconvolutionintegral operators. |
| spellingShingle | Khalida Inayat Noor On certain classes of close-to-convex functions International Journal of Mathematics and Mathematical Sciences univalent close-to-convex starlike convolution integral operators. |
| title | On certain classes of close-to-convex functions |
| title_full | On certain classes of close-to-convex functions |
| title_fullStr | On certain classes of close-to-convex functions |
| title_full_unstemmed | On certain classes of close-to-convex functions |
| title_short | On certain classes of close-to-convex functions |
| title_sort | on certain classes of close to convex functions |
| topic | univalent close-to-convex starlike convolution integral operators. |
| url | http://dx.doi.org/10.1155/S0161171293000390 |
| work_keys_str_mv | AT khalidainayatnoor oncertainclassesofclosetoconvexfunctions |